Geodesic
Vector-valued ergodic theorems for multiparameter Additive processes II
Ryotaro Sato1
1 Department of Mathematics Okayama University Okayama, 700-8530 Japan
Colloquium Mathematicum, Tome 97 (2003) no. 1, pp. 117-129 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Previously we obtained stochastic and pointwise ergodic theorems for a continuous $d$-parameter additive process $F$ in $L_{1}(({\mit\Omega},{\mit\Sigma},\mu);X)$, where $X$ is a reflexive Banach space, under the condition that $F$ is bounded. In this paper we improve the previous results by considering the weaker condition that the function $W(\cdot)= \mathop{\rm ess\,sup} \{ \|F(I)(\cdot)\| : I\subset [0, 1)^{d}\}$ is integrable on ${\mit\Omega}$.
DOI : 10.4064/cm97-1-11
Keywords: previously obtained stochastic pointwise ergodic theorems continuous d parameter additive process mit omega mit sigma where reflexive banach space under condition bounded paper improve previous results considering weaker condition function cdot mathop ess sup cdot subset integrable mit omega

Ryotaro Sato 1

1 Department of Mathematics Okayama University Okayama, 700-8530 Japan 
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Ryotaro Sato. Vector-valued ergodic theorems
 for multiparameter Additive processes II. Colloquium Mathematicum, Tome 97 (2003) no. 1, pp. 117-129. doi: 10.4064/cm97-1-11

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